堆及其工作集
Heaps and Their Working Sets
AI总结：
研究构建具有强大性能保证的堆，通过证明现有工作集界限概念等价简化理论，提出首个有摊还栈状界限、支持特定时间操作的堆实现，扩展堆应用范围并提升性能。
AI中文摘要：
我们构建了一个具有强大的超出最坏情况性能保证的堆，并探索对这类堆的分析。首先，通过证明本质上所有现有堆的工作集界限概念都是等价的（除了严格更强的所谓栈状界限），统一了这些概念，简化了理论框架并扩展了工作集界限堆的应用范围。其次，我们提出了首个具有摊还栈状界限、支持\(\mathcal O(1)\)时间的键值减小操作和\(o(\log^*n)\)时间的插入操作的堆实现。
英文摘要：
We construct a heap with strong beyond-worst-case performance guarantees and explore the analysis of such heaps. First, we unify existing notions of the working-set bound for heaps by proving that essentially all of them are equivalent - with the notable exception of the so-called stack-like bound, which is strictly stronger. This equivalence simplifies the theoretical landscape and extends the range of applications of heaps with working-set bounds. Second, we present the first heap implementation that has the amortized stack-like bound and supports $\mathcal O(1)$-time decrease-key and $o(\log^*n)$-time insert.
